to treat well, to detain, article, friendship
欵 centers on positive interpersonal connection: treating someone well, showing friendship, or extending hospitality. The sense of detaining or an article likely derives from the idea of holding someone in a friendly manner or a written item that formalizes a bond.
The exact historical development of 欵 is uncertain. It appears to combine 欠 (open mouth, lack) with a left side that may be a variant of 款's left component, but the original semantic and phonetic roles are unclear.
The left side looks like a person (匕) with an arrow (矢), and the right side is an open mouth (欠). Imagine treating a guest well by offering them food and drink, so they feel friendship and stay a while.
For カン, picture a can of friendship: you open a can (カン) of soda to share with a friend, treating them well and strengthening your bond.